Title:
Detrending career statistics in professional baseball: Accounting for the steroids era and beyond

Abstract: There is a long standing debate over how to objectively compare the career
achievements of professional athletes from different historical eras.
Developing an objective approach will be of particular importance over the next
decade as Major League Baseball (MLB) players from the "steroids era" become
eligible for Hall of Fame induction. Here we address this issue, as well as the
general problem of comparing statistics from distinct eras, by detrending the
seasonal statistics of professional baseball players. We detrend player
statistics by normalizing achievements to seasonal averages, which accounts for
changes in relative player ability resulting from both exogenous and endogenous
factors, such as talent dilution from expansion, equipment and training
improvements, as well as performance enhancing drugs (PED). In this paper we
compare the probability density function (pdf) of detrended career statistics
to the pdf of raw career statistics for five statistical categories -- hits
(H), home runs (HR), runs batted in (RBI), wins (W) and strikeouts (K) -- over
the 90-year period 1920-2009. We find that the functional form of these pdfs
are stationary under detrending. This stationarity implies that the statistical
regularity observed in the right-skewed distributions for longevity and success
in professional baseball arises from both the wide range of intrinsic talent
among athletes and the underlying nature of competition. Using this simple
detrending technique, we examine the top 50 all-time careers for H, HR, RBI, W
and K. We fit the pdfs for career success by the Gamma distribution in order to
calculate objective benchmarks based on extreme statistics which can be used
for the identification of extraordinary careers.